Compressive Response of Pyramidal Lattices Embedded in Foams

Abstract

Recent endeavors to combine the desirable energy-absorption characteristics of stochastic foams with the comparatively high strengths of pyramidal lattices have shown promise for creating composites that outperform their constituents alone under compressive loading. Herein we employ numerical and analytical models to identify both the mechanisms by which synergistic behavior is obtained in such composites and the constituent mass fractions that yield maximum benefits. We find that the loading boundary conditions piay a crucial role. When, for instance, composites are loaded between plates that are well bonded to the composites, their specific strengths invariably exceed those predicted by a rule-of-mixtures; however, these strengths can always be improved through an optimized lattice of equivalent mass. In contrast, when the composites are loaded betu'een frictionless plates, their specific strengths exceed not only rule-of-mixtures predictions but, in many cases, aiso that of any mass-equivalent pyramidal lattice alone subject to the same (frictionless) conditions. The origin of this behavior is found to arise from foamstabilization of lattice bending and splaying: deformation modes that govern strength in the absence of foam. In essence, the foam causes a transition from bend-dominated to stretch-dominated behavior in the lattice.

Influence of processing conditions on strut structure and compressive properties of cellular lattice structures fabricated by selective laser melting

“…11d that the normalised nominal yield strength (σ o =σ o ) increases continuously with relative density, which is consistent with previous work [27][28][29]. However, relative density does not seem to be the only factor influencing the compression strengths given that the effective normalised nominal yield strength (σ o =σ o ρ) in Fig.…”

Optimization of Additively Manufactured Multi-Material Lattice Structures Using Generalized Optimality Criteria

“…Equations (12) and (14) yield a set of Lagrangian multipliers that if all negative indicate an independent set of constraints. The necessary condition is that is non-singular and that is positive definite.…”

“…The necessary condition is that is non-singular and that is positive definite. If Equation 14yields both positive and negative Lagrangian multipliers, then the positive multipliers indicate constraint dependency requiring their deletion from the active constraint set and recalculation of (14) repeating the procedure until multipliers are all negative.…”

“…Lattice structures are growing in interest due to their improved strength-to-weight ratio compared with stochastic foams alone. When combined with stochastic foams, hybrid lattice-foam structures may show superior performance for both strength and energy absorption under certain conditions [14]. A complete DfAM process for designing a customized product, such as a sports helmet with multi-material lattices, includes phases for characterizing AM materials and processes, developing quantitative and simulation models based on this characterization, optimizing designs with computational methods, and then fabricating and testing the final multimaterial product (Fig.…”

A Generalized Optimality Criteria Method for Optimization of Additively Manufactured Multimaterial Lattice Structures

“…Lattice structures are growing in interest due to their improved strength-to-weight ratio compared with stochastic foams alone. When lattices are utilized in combination with stochastic foams, the combination sometimes shows superior performance for both strength and energy absorption, which are both necessary for effective helmet performance [15]. Additionally, AM processes enable the construction of lattices tailored for specific products that were not achievable with past manufacturing methods.…”